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Answer :
To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the line that would be perpendicular to it.
1. Understand Perpendicular Slopes: Perpendicular lines in geometry have slopes that are negative reciprocals of each other. This means if you have a slope [tex]\(m\)[/tex], the perpendicular slope will be [tex]\(-\frac{1}{m}\)[/tex].
2. Calculate the Perpendicular Slope: Here, the given slope is [tex]\(-\frac{5}{6}\)[/tex]. To find the perpendicular slope, take the negative reciprocal:
[tex]\[
\text{Perpendicular slope} = -\left(\frac{1}{-\frac{5}{6}}\right)
\][/tex]
This simplifies to:
[tex]\[
\text{Perpendicular slope} = \frac{6}{5}
\][/tex]
The negative reciprocal changes the sign, and you swap the numerator and denominator.
3. Conclusion: A line that is perpendicular to another line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex], which can also be written as 1.2 in decimal form.
Thus, if you want to verify which of the lines (JK, LM, NO, PQ) has a slope of 1.2, you would need additional information about the slopes of these specific lines to identify the correct answer.
1. Understand Perpendicular Slopes: Perpendicular lines in geometry have slopes that are negative reciprocals of each other. This means if you have a slope [tex]\(m\)[/tex], the perpendicular slope will be [tex]\(-\frac{1}{m}\)[/tex].
2. Calculate the Perpendicular Slope: Here, the given slope is [tex]\(-\frac{5}{6}\)[/tex]. To find the perpendicular slope, take the negative reciprocal:
[tex]\[
\text{Perpendicular slope} = -\left(\frac{1}{-\frac{5}{6}}\right)
\][/tex]
This simplifies to:
[tex]\[
\text{Perpendicular slope} = \frac{6}{5}
\][/tex]
The negative reciprocal changes the sign, and you swap the numerator and denominator.
3. Conclusion: A line that is perpendicular to another line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex], which can also be written as 1.2 in decimal form.
Thus, if you want to verify which of the lines (JK, LM, NO, PQ) has a slope of 1.2, you would need additional information about the slopes of these specific lines to identify the correct answer.
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